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Logical foundations of objectoriented and framebased languages
 JOURNAL OF THE ACM
, 1995
"... We propose a novel formalism, called Frame Logic (abbr., Flogic), that accounts in a clean and declarative fashion for most of the structural aspects of objectoriented and framebased languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, ..."
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Cited by 763 (59 self)
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We propose a novel formalism, called Frame Logic (abbr., Flogic), that accounts in a clean and declarative fashion for most of the structural aspects of objectoriented and framebased languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, encapsulation, and others. In a sense, Flogic stands in the same relationship to the objectoriented paradigm as classical predicate calculus stands to relational programming. Flogic has a modeltheoretic semantics and a sound and complete resolutionbased proof theory. A small number of fundamental concepts that come from objectoriented programming have direct representation in Flogic; other, secondary aspects of this paradigm are easily modeled as well. The paper also discusses semantic issues pertaining to programming with a deductive objectoriented language based on a subset of Flogic.
HiLog: A foundation for higherorder logic programming
 JOURNAL OF LOGIC PROGRAMMING
, 1993
"... We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higherorder syntax and allows arbitrary terms to appear in places where predicates, functions and atomic formulas occur in predicate calc ..."
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Cited by 213 (40 self)
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We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higherorder syntax and allows arbitrary terms to appear in places where predicates, functions and atomic formulas occur in predicate calculus. But its semantics is firstorder and admits a sound and complete proof procedure. Applications of HiLog are discussed, including DCG grammars, higherorder and modular logic programming, and deductive databases.
Theory of Generalized Annotated Logic Programming and its Applications
 Journal of Logic Programming
, 1992
"... Annotated logics were introduced in [43] and later studied in [5, 7, 31, 32]. In [31], annotations were extended to allow variables and functions, and it was argued that such logics can be used to provide a formal semantics for rulebased expert systems with uncertainty. In this paper we continue to ..."
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Cited by 170 (21 self)
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Annotated logics were introduced in [43] and later studied in [5, 7, 31, 32]. In [31], annotations were extended to allow variables and functions, and it was argued that such logics can be used to provide a formal semantics for rulebased expert systems with uncertainty. In this paper we continue to investigate the power of this approach. First, we introduce a new semantics for such programs based on ideals of lattices. Subsequently, some proposals for multivalued logic programming [5, 7, 32, 47, 40, 18] as well as some formalisms for temporal reasoning [1, 3, 42] are shown to fit into this framework. As an interesting byproduct of this investigation, we obtain a new result concerning multivalued logic programming: a model theory for Fitting's bilatticebased logic programming, which until now has not been characterized modeltheoretically. This is accompanied by a corresponding proof theory. 1 Introduction Large knowledge bases can be inconsistent in many ways. Nevertheless, certain...
The Value of the Four Values
 Artificial Intelligence
, 1998
"... In his wellknown paper "How computer should think" ([Be77b]) Belnap argues that four valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the fourvalued structure has among Ginsberg's wellknown bilatti ..."
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Cited by 62 (6 self)
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In his wellknown paper "How computer should think" ([Be77b]) Belnap argues that four valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the fourvalued structure has among Ginsberg's wellknown bilattices is similar to the role that the twovalued algebra has among Boolean algebras. Specifically, we provide several theorems that show that the most useful bilatticevalued logics can actually be characterized as fourvalued inference relations. In addition, we compare the use of threevalued logics with the use of fourvalued logics, and show that at least for the task of handling inconsistent or uncertain information, the comparison is in favor of the latter. Keyworkds: Bilattices, Paraconsistency, Multiplevalued systems, Preferential logics, Reasoning. 1 Introduction In [Be77a, Be77b] Belnap introduced a logic intended to deal in a useful way with inconsistent and incomplete information....
Probabilistic Deductive Databases
, 1994
"... Knowledgebase (KB) systems must typically deal with imperfection in knowledge, e.g. in the form of imcompleteness, inconsistency, uncertainty, to name a few. Currently KB system development is mainly based on the expert system technology. Expert systems, through their support for rulebased program ..."
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Cited by 57 (2 self)
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Knowledgebase (KB) systems must typically deal with imperfection in knowledge, e.g. in the form of imcompleteness, inconsistency, uncertainty, to name a few. Currently KB system development is mainly based on the expert system technology. Expert systems, through their support for rulebased programming, uncertainty, etc., offer a convenient framework for KB system development. But they require the user to be well versed with the low level details of system implementation. The manner in which uncertainty is handled has little mathematical basis. There is no decent notion of query optimization, forcing the user to take the responsibility for an efficient implementation of the KB system. We contend KB system development can and should take advantage of the deductive database technology, which overcomes most of the above limitations. An important problem here is to extend deductive databases into providing a systematic basis for rulebased programming with imperfect knowledge. In this paper, we are interested in an exension handling probabilistic knowledge.
Reasoning with Logical Bilattices
, 1995
"... . The notion of bilattice was introduced by Ginsberg, and further examined by Fitting, as a general framework for many applications. In the present paper we develop proof systems, which correspond to bilattices in an essential way. For this goal we introduce the notion of logical bilattices. We als ..."
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Cited by 55 (9 self)
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. The notion of bilattice was introduced by Ginsberg, and further examined by Fitting, as a general framework for many applications. In the present paper we develop proof systems, which correspond to bilattices in an essential way. For this goal we introduce the notion of logical bilattices. We also show how they can be used for efficient inferences from possibly inconsistent data. For this we incorporate certain ideas of Kifer and Lozinskii, which happen to suit well the context of our work. The outcome are paraconsistent logics with a lot of desirable properties 1 . 1. Introduction When using multiplevalued logics, it is usual to order the truth values in a lattice structure. In most cases such a partial order intuitively reflects differences in the "measure of truth" that the lattice elements are supposed to represent. There exist, however, other intuitive criteria of ordering that might be useful. Another reasonable ordering might reflect, for example, differences in the amoun...
FLORA2: A RuleBased Knowledge Representation and Inference Infrastructure for the Semantic Web
 In Second International Conference on Ontologies, Databases and Applications of Semantics (ODBASE
, 2003
"... Abstract. Flora2 is a rulebased objectoriented knowledge base system designed for a variety of automated tasks on the Semantic Web, ranging from metadata management to information integration to intelligent agents. The Flora2 system integrates Flogic, HiLog, and Transaction Logic into a cohere ..."
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Cited by 55 (5 self)
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Abstract. Flora2 is a rulebased objectoriented knowledge base system designed for a variety of automated tasks on the Semantic Web, ranging from metadata management to information integration to intelligent agents. The Flora2 system integrates Flogic, HiLog, and Transaction Logic into a coherent knowledge representation and inference language. The result is a flexible and natural framework that combines rulebased and objectoriented paradigms. This paper discusses the principles underlying the design of the Flora2 system and describes its salient features, including metaprogramming, reification, logical database updates, encapsulation, and support for dynamic modules. 1
A Parametric Approach to Deductive Databases with Uncertainty
, 1997
"... Numerous frameworks have been proposed in recent years for deductive databases with uncertainty. These frameworks differ in (i) their underlying notion of uncertainty, (ii) the way in which uncertainties are manipulated, and (iii) the way in which uncertainty is associated with the facts and rules o ..."
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Cited by 44 (6 self)
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Numerous frameworks have been proposed in recent years for deductive databases with uncertainty. These frameworks differ in (i) their underlying notion of uncertainty, (ii) the way in which uncertainties are manipulated, and (iii) the way in which uncertainty is associated with the facts and rules of a program. On the basis of (iii), these frameworks can be classified into implication based (IB) and annotation based (AB) frameworks. In this paper, we develop a generic framework called the parametric framework as a unifying umbrella for IB frameworks. We develop the declarative, fixpoint, and prooftheoretic semantics of programs in the parametric framework and show their equivalence. Using this framework as a basis, we study the query optimization problem of containment of conjunctive queries in this framework, and establish necessary and sufficient conditions for containment for several classes of parametric conjunctive queries. Our results yield tools for use in the query optimization for large classes of query programs in IB deductive databases with uncertainty.
A Logic For Programming Database Transactions
, 1998
"... : We propose an extension of classical predicate calculus, called Transaction Logic, which provides a logical foundation for the phenomenon of state changes in logic programs and databases. Transaction Logic comes with a natural model theory and a sound and complete proof theory. The proof theory n ..."
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Cited by 42 (22 self)
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: We propose an extension of classical predicate calculus, called Transaction Logic, which provides a logical foundation for the phenomenon of state changes in logic programs and databases. Transaction Logic comes with a natural model theory and a sound and complete proof theory. The proof theory not only verifies programs, but also executes them, which makes this logic an ideal tool for declarative programming of database transactions and statemodifying logic programs. The semantics of Transaction Logic leads naturally to features whose amalgamation in a single logic has proved elusive in the past. These features include hypothetical and committed updates, dynamic constraints on transaction execution, nondeterminism, and bulk updates. Finally, Transaction Logic holds promise as a logical model of hitherto nonlogical phenomena, including socalled procedural knowledge in AI, and the behavior of objectoriented databases, especially methods with side effects. This paper presents the...
Answer Sets for Consistent Query Answering in Inconsistent Databases
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2003
"... A relational database is inconsistent if it does not satisfy a given set of integrity constraints. Nevertheless, it is likely that most of the data in it is consistent with the constraints. In this paper we apply logic programming based on answer sets to the problem of retrieving consistent informat ..."
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Cited by 38 (8 self)
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A relational database is inconsistent if it does not satisfy a given set of integrity constraints. Nevertheless, it is likely that most of the data in it is consistent with the constraints. In this paper we apply logic programming based on answer sets to the problem of retrieving consistent information from a possibly inconsistent database. Since consistent information persists from the original database to every of its minimal repairs, the approach is based on a specification of database repairs using disjunctive logic programs with exceptions, whose answer set semantics can be represented and computed by systems that implement stable model semantics. These programs allow us to declare persistence by default of data from the original instance to the repairs; and changes to restore consistency, by exceptions. We concentrate mainly on logic programs for binary integrity constraints, among which we find most of the integrity constraints found in practice.